Polygamy is one of the few practices that still evoke genuine disgust in people. It’s a watchword for ignorance, sexual depredation, oppression of women and weird, culty outfits. But spurred on by the same-sex marriage debate and more-sympathetic portrayals of polygamists and polyamorists in our larger culture, some plural families are coming out of the shadows and beginning to advocate for their way of life.

One of these families, the Dargers, independent fundamentalist Mormons, invited me into their home to check out how they live. I report about it in the Aug. 6 issue of TIME, which subscribers can read here. The Dargers are a model non-monogamous family. They’re attractive, they dress well, and they labor mightily to provide for their 23 kids.

This helps because their setup is pretty weird: Joe, the patriarch, is married to three women, two of whom are identical twin sisters. He married one of those sisters (Vicki) and another woman (Alina) at the same time, after dating them at the same time, all at the women’s consent. It gets weirder. Val, the other twin, was married to another polygamous guy and had five kids with him before she fled. Vicki and Alina told Joe that he should marry her too, they say. So he did.

But for a deeply unconventional family, they look pretty normal. (Watch a video about their life here.) They live together in a cheerfully messy house outside Salt Lake City, with three master bedrooms, boatloads of items bought in bulk and eye-watering amounts of laundry.

Unlike the adherents of more closed fundamentalist Mormon sects, like the Fundamentalist Church of Jesus Christ of Latter-day Saints, headed by Warren Jeffs, the Dargers are independent fundamentalists, sort of Polygamists 2.0. The way they live is a felony in Utah, but nobody is coming after them. (Arizona tried that in 1953, with rather dire results, documented in this fantastic LIFE photo-essay.)

The Dargers and Kody Brown’s family, who star in the TLC reality show Sister Wives and wrote the New York Times best seller Becoming Sister Wives, are on the front line of a campaign to destigmatize multipartner unions. Flanking them is a growing number of more vocal polyamorists — people who have multiple lovers by mutual consent. (Polyamorists have recently gotten their own reality show too.)

So, should polygamy be more accepted? As society re-examines what the institution of marriage is, should polygamy get a look-in? Who does polygamy really hurt? As it turns out, it’s not who you think.